Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs
Abstract
We study entropy-regularized linear programs with sparse affine constraints and compare two exact dual representations induced by whether a redundant normalization constraint is retained or eliminated. Eliminating it yields a partially separable sum-exp dual with sparse affine factors but unbounded curvature. Our main result is an accelerated randomized block method whose acceleration preserves sparse data-access cost. The key ingredient is a global entropy-specific Hessian--gap bound that remains valid for signed constraint matrices, admits computable block-overlap refinements, and provides deterministic curvature certificates before sampling. This geometry supports square-root importance sampling and an exact lazy implementation in which sparse arithmetic cost is weighted by local curvature rather than by a worst-block factor. We further introduce a gap-dependent curvature dimension that connects the generalized-smooth regime to the classical effective-rank intuition for coordinate methods. Retaining the normalization constraint yields a log-sum-exp dual with globally bounded higher derivatives, enabling gradient-regularized and cubic-regularized Newton methods. Experiments compare the resulting methods in terms of coordinate epochs, arithmetic operations, and wall-clock time, separating the effects of acceleration, touched-data sparsity, and problem-specific structure.
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BibTeX
@misc{podlipnova2026smooth,
title = {{Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs}},
author = {Irina Podlipnova and Maxim Mashtaler and Artem Agafonov and Yuriy Dorn and Alexander Gasnikov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32558},
eprint = {2609.32558},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32558},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs
AU - Irina Podlipnova
AU - Maxim Mashtaler
AU - Artem Agafonov
AU - Yuriy Dorn
AU - Alexander Gasnikov
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32558
UR - https://arxiv.org/abs/2609.32558
AB - We study entropy-regularized linear programs with sparse affine constraints and compare two exact dual representations induced by whether a redundant normalization constraint is retained or eliminated. Eliminating it yields a partially separable sum-exp dual with sparse affine factors but unbounded curvature. Our main result is an accelerated randomized block method whose acceleration preserves sparse data-access cost. The key ingredient is a global entropy-specific Hessian--gap bound that remains valid for signed constraint matrices, admits computable block-overlap refinements, and provides deterministic curvature certificates before sampling. This geometry supports square-root importance sampling and an exact lazy implementation in which sparse arithmetic cost is weighted by local curvature rather than by a worst-block factor. We further introduce a gap-dependent curvature dimension that connects the generalized-smooth regime to the classical effective-rank intuition for coordinate methods. Retaining the normalization constraint yields a log-sum-exp dual with globally bounded higher derivatives, enabling gradient-regularized and cubic-regularized Newton methods. Experiments compare the resulting methods in terms of coordinate epochs, arithmetic operations, and wall-clock time, separating the effects of acceleration, touched-data sparsity, and problem-specific structure.
ER -